In a skillet over medium heat, cook the ground beef and chopped onion with salt and black pepper until the beef is browned and the onion is translucent.
Stir in the salsa and cook for an additional 2 minutes, then remove from heat and let the mixture cool slightly.
Lay out the flour tortillas and distribute the beef mixture evenly among them, leaving room at the edges for folding.
Sprinkle each with a generous amount of cheddar cheese.
Fold the tortillas burrito-style, tucking in the ends and rolling them tightly to secure the filling.
Heat the vegetable oil in a deep fryer or large pot to 375°F.
Carefully place the burritos in the hot oil and fry until they are golden brown and crispy, about 3-4 minutes per side.
Remove the fried burritos with a slotted spoon and drain on paper towels.
Serve hot with your choice of sides or dipping sauces.